Constrained investment-reinsurance optimization with regime switching under variance premium principle

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• 作者：Lv Chen^a ; ^{chenlvhero@sina.com} ; Linyi Qian^a ; ^{lyqian@stat.ecnu.edu.cn} ; Yang Shen^b ; ^{skyshen87@gmail.com} ; Wei Wang^c ; ^{wswang2008@163.com}
• 关键词：Investment ; Reinsurance ; Regime switching ; Variance premium principle ; Hamilton&ndash ; Jacobi&ndash ; Bellman equation
• 刊名：Insurance: Mathematics and Economics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：71
• 期：Complete
• 页码：253-267
• 全文大小：613 K
• 卷排序：71

文摘

This paper studies optimal investment and reinsurance problems for an insurer under regime-switching models. Two types of risk models are considered, the first being a Markov-modulated diffusion approximation risk model and the second being a Markov-modulated classical risk model. The insurer can invest in a risk-free bond and a risky asset, where the underlying models for investment assets are modulated by a continuous-time, finite-state, observable Markov chain. The insurer can also purchase proportional reinsurance to reduce the exposure to insurance risk. The variance principle is adopted to calculate the reinsurance premium, and Markov-modulated constraints on both investment and reinsurance strategies are considered. Explicit expressions for the optimal strategies and value functions are derived by solving the corresponding regime-switching Hamilton–Jacobi–Bellman equations. Numerical examples for optimal solutions in the Markov-modulated diffusion approximation model are provided to illustrate our results.